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Volume 31, Issue 2 Volume 31, Issue 2 Competing impure public goods and the sustainability of the theater arts Tyler Pugliese Jeffrey Wagner Economics Dept., Rochester Institute of Technology Economics Dept., Rochester Institute of Technology Abstract The general purpose of this paper is to extend the literature regarding public good provision when consumers may contribute via consumption of an impure public good and/or by donating directly to the public good. Standard models pose consumer utility as a function of one impure public good and one or more private goods. Our model features two competing impure public goods and two private goods: one that is a conventional substitute good and one that is a numeraire. We build most directly upon Kotchen's (2005) model of “green” consumption of impure public goods. We propose national and local live theater arts as an example of competing impure public goods. Our model shows that if local and national live theater are substitutes, and the national live theater (such as the Met) is strengthened via technological change (for instance, via simulcasts into local venues), the overall sustainability of the live theater arts may be diminished. We are grateful to Editor John Conley; an anonymous referee; session participants at the 2010 New York State Economics Association annual meeting (and particularly our discussant, Bill Kolberg); and session participants at the 2011 Midwest Economics Association annual meeting (and particularly our discussant, Carly Urban) for several helpful and encouraging comments. Citation: Tyler Pugliese and Jeffrey Wagner, (2011) ''Competing impure public goods and the sustainability of the theater arts'', Economics Bulletin, Vol. 31 no.2 pp. 1295-1303. Submitted: Feb 18 2011. Published: April 27, 2011. 1. Introduction There is a rich literature regarding the economics of public good provision when consumers may contribute by consuming a product that jointly yields private and public benefits and/or by making a donation that directly supports the public good. The economics of contributing via consumption of a joint/mixed/impure product was set forth by Cornes and Sandler (1984, 1994). The impact of a donation mechanism alongside joint production was analyzed by Andreoni (1989, 1990) and Vicary (1997, 2000). Most recently, Kotchen (2005) extended this literature with a model in which consumers choose among three products: a numeraire good, an impure public good that generates both a private and public characteristic, and a private conventional good substitute for the impure public good that generates only the private characteristic. He then adds the donation possibility to this generalization and conducts comparative statics analysis within the extended framework. Although Kotchen’s model generates a number of insights, all of the aforementioned models feature a single impure public good competing against one or more private goods. The general purpose of this paper is to extend this line of inquiry to a framework in which consumers allocate consumption and donation resources among private goods and two competing impure public goods. We find that the seemingly straightforward step of adding a second impure public good to the consumer choice framework greatly complicates the comparative statics results. While this is in some sense discouraging, the generalized model nevertheless enables us to point to specific sources of the complications that can arise in real-world policy-making. While the extension we pursue is of theoretical interest, we were motivated to explore it by a specific empirical question: Could the New York Metropolitan Opera’s relatively recent deployment of live simulcasts in hundreds of theaters across the U.S. be expected to strengthen or weaken local theater arts quantity/quality, and therefore strengthen or weaken the long-run sustainability of the theater arts in general?1 As Baumol and Bowen (1966) forewarned, technological progress presents something of a double-edged sword to the sustainability of the theater arts, not unlike the challenge technological progress poses to environmental quality and other public goods. On one hand, the popularity of such technologically sophisticated Met simulcasts can be taken as evidence that the sustainability of the theater arts has been enhanced. On the other hand, if such simulcasts from a national institution drive live local theater from the market, the effect of simulcast technology on the overall sustainability of theater arts is ambiguous. Our instinct is that the Met and local theater productions can be considered competing impure public goods, and that therefore a conceptual structure like Kotchen’s, extended to two impure public goods, could help us understand how a number of exogenous factors combine to affect the sustainability of the theater arts. Our resulting model confirms that if local and national live theater are substitutes, and the national live theater (such as the Metropolitan Opera of New York and its simulcasts into local venues) is strengthened via technological change, the overall sustainability of the live theater arts may be diminished. 2. Basic Concepts and Notation We proceed by setting forth Kotchen’s basic framework and then we introduce the notation for the second impure public good. Kotchen follows Cornes and Sandler (1984, 1994) in 1 Recent data suggests that 1.8 million tickets to simulcasts were sold in 2009 and sales were on pace to surpass 2.25 million in 2010. http://online.wsj.com/article/SB10001424052702303695604575182474127585754.html?mod=WSJ_newsreel_lifeStyle. 1 utilizing the characteristics approach to consumer demand that was developed by Gorman (1980) and Lancaster (1971). Consider a representative consumer who has well-defined preferences U over four characteristics: X, Y, W, and Z. Characteristic X could be mass media entertainment or caffeine that is generated by consumption of conventional private goods such as movie theater tickets in the former case and by coffee in the latter (Kotchen) case. Characteristic Y is theatrical arts quality, cultural quality, or environmental quality on a broad, national scale that is provided by impure public goods such as the New York Metropolitan Opera in the former case or by shade-grown coffee in the latter case. Characteristic Y is valued by consumers to the extent that it captures what national arts endeavors such as the Met generate in utility to consumers in the current generation, as well as what they preserve for consumption by future generations on a national (if not global) level. We contrast this source of utility from national public goods with characteristic W, which represents what is valued by consumers in local theater arts in the former case and local environmental quality in the latter case. Characteristic W captures what consumers feel is distinctive about live theater focused upon local issues and produced by local artists. Such productions therefore yield local benefits as well as public benefits that are passed to future generations and become part of the national arts legacy. It is of course true that citizens of New York City may view the Met as a “local” theater; however, our belief is that local support for the Met is not so much with regard to preserving local theater as it is for preserving the Met as a national institution that produces and preserves theater that resonates in every state and village. Finally, following Kotchen, we define characteristic Z as capturing in a numeraire manner all other characteristics of value to the consumer beyond characteristics X, Y, and W. Turning now to the goods that generate these characteristics, we follow Kotchen in allowing for the impure public goods to generate multiple characteristics in (constant) linear fashion. Good l (local live theater) generates characteristics X, Y and W according to: X = α l l (1) Y = β l l (2) W = γl (3) Good n (national live theater) generates characteristics X and Y (and not W) according to: X = α n n (4) Y = β n n (5) Good c (conventional good such as movie tickets or DVDs) generates only characteristic X: X = c (6) Good z (numeraire good) generates only characteristic Z: Z = z (7) The last element in the set-up to note, again following Kotchen, is that since goods l and n are impure public goods, the representative consumer gains utility from others’ provision of these goods. Thus, the amounts of Y and W that are produced are given by the sums of what the representative agent chooses and what all other agents choose. The notation for this aspect will be specified below, where we set forth the representative agent’s maximization problem. 3. Optimal Choices in the Presence of a Conventional Substitute We follow Kotchen in this section by introducing a conventional substitute to our model in which a representative consumer has exogenous income m to allocate across that conventional good, a numeraire good, and two impure public goods (one local and one national). Given our assumptions, the consumer’s problem is: 2 Max{U (Z, X ,Y,W )Z + Pc c + Pl l + Pn n = m} with (8) X = c + α l l + α n n (9) ~ Y = β l l + β n n + Y (10) ~ W = γl +W (11) As in Cornes and Sandler (1984) and Kotchen (2005), it is advantageous here to transform the problem from goods space to characteristics space, so that the demands for the characteristics can be derived as functions of public good contributions from others. To do so in our model, we rearrange (9), (10) and (11) to obtain: c = X −α l l −α n n (9’) ~ Y − β l − Y n = l (10’) β n ~ W −W l = (11’) γ ~ ~ where Y and W are exogenously provided.2 Substituting into (8), we obtain the two-impure- public-good analogue to Kotchen’s eq. (2): α n β l Pc Pcα l Pl Pn βl Pn α n Pc MaxU (Z, X ,Y,W )Z + XPc +W − + − + Y − = β γ γ γ β γ β β n n n n ~ α n β l Pc Pcα l Pl Pn β l ~ Pn α n Pc m +W − + − + Y − (12) β nγ γ γ β nγ β n β n Note that in Kotchen’s eq.
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